In one dimension collisions are inevitable, so it suffices to consider point particles. The point particles make the system infinitely diluted and hence ideal with the well-known equation of state. The case with equal masses is pathological — each collision leads to the exchange of identities, with no relaxation. To avoid pathology, we consider a hard point gas with binary mass distribution and assume that particles with dissimilar masses alternate. This system is non-integrable, has good thermalization behavior, and continues to have an ideal gas equation of state. The alternating hard particle (AHP) gas has been extensively investigated in the context of studies on heat transport and hydrodynamics in one dimension [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. In recent work [12]}, [13]}, the AHP model was used for
a numerical verification of the equivalence of the continuum hydrodynamics description and the Newtonian description in the context of the so-called blast problem. The blast problem is similar to the splash problem with the important difference that energy is injected at the centre of a cold gas. The long time behavior of the blast is described by hydrodynamics. The work in [12]}, [13]} find that the bulk of the excited gas is described by the famous Taylor-von Neumann-Sedov (TvNS) self-similar solution of the Euler equations, while Navier-Stokes corrections become important in the core region. The splash problem is less tractable than the blast problem due to the lack of symmetry.
